The Laplace-Beltrami operator expressed in terms of fermionic-type creation and annihilation operators

Several operator relations for differential operators on a Riemannian manifold are written down in terms of a set of basis operators which act on an exterior algebra. Differential geometric relations are expressed in terms of these operators. An important relation which connects the Laplace-Beltrami operator on p-forms to the Bochner Laplacian is developed